Question

find the midpoint of the line segment with the given endpoints. (2,10) and (8,4) the midpoint of the segment is (type an ordered pair.)

Explanation:

Step1: Find the x - coordinate of the midpoint

The formula for the x - coordinate of the midpoint \(M_x\) of two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M_x=\frac{x_1 + x_2}{2}\).
Here, \(x_1 = 2\), \(x_2=8\), so \(M_x=\frac{2 + 8}{2}=\frac{10}{2}=5\).

Step2: Find the y - coordinate of the midpoint

The formula for the y - coordinate of the midpoint \(M_y\) of two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M_y=\frac{y_1 + y_2}{2}\).
Here, \(y_1 = 10\), \(y_2 = 4\), so \(M_y=\frac{10+4}{2}=\frac{14}{2}=7\).

Answer:

\((5,7)\)